<div class="problem-statement">
 <div class="header">
  <div class="title">
   D. K-good
  </div>
  <div class="time-limit">
   <div class="property-title">
    time limit per test
   </div>3 seconds
  </div>
  <div class="memory-limit">
   <div class="property-title">
    memory limit per test
   </div>256 megabytes
  </div>
  <div class="input-file">
   <div class="property-title">
    input
   </div>standard input
  </div>
  <div class="output-file">
   <div class="property-title">
    output
   </div>standard output
  </div>
 </div>
 <div>
  <p>We say that a positive integer $n$ is $k$-good for some positive integer $k$ if $n$ can be expressed as a sum of $k$ positive integers which give $k$ distinct remainders when divided by $k$.</p>
  <p>Given a positive integer $n$, find some $k \geq 2$ so that $n$ is $k$-good or tell that such a $k$ does not exist.</p>
 </div>
 <div class="input-specification">
  <div class="section-title">
   Input
  </div>
  <p>The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^5$) — the number of test cases.</p>
  <p>Each test case consists of one line with an integer $n$ ($2 \leq n \leq 10^{18}$).</p>
 </div>
 <div class="output-specification">
  <div class="section-title">
   Output
  </div>
  <p>For each test case, print a line with a value of $k$ such that $n$ is $k$-good ($k \geq 2$), or $-1$ if $n$ is not $k$-good for any $k$. If there are multiple valid values of $k$, you can print any of them.</p>
 </div>
 <div class="sample-tests">
  <div class="section-title">
   Example
  </div>
  <div class="sample-test">
   <div class="input">
    <div class="title">
     Input
    </div>
    <pre>5
2
4
6
15
20
</pre>
   </div>
   <div class="output">
    <div class="title">
     Output
    </div>
    <pre>-1
-1
3
3
5
</pre>
   </div>
  </div>
 </div>
 <div class="note">
  <div class="section-title">
   Note
  </div>
  <p>$6$ is a $3$-good number since it can be expressed as a sum of $3$ numbers which give different remainders when divided by $3$: $6 = 1 + 2 + 3$.</p>
  <p>$15$ is also a $3$-good number since $15 = 1 + 5 + 9$ and $1, 5, 9$ give different remainders when divided by $3$.</p>
  <p>$20$ is a $5$-good number since $20 = 2 + 3 + 4 + 5 + 6$ and $2,3,4,5,6$ give different remainders when divided by $5$.</p>
 </div>
</div>